169 Rania Mosaad Saad Furniture design inspired from fractals. Dr. Rania Mosaad Saad Assistant Professor, Interior Design and Furniture Department, Faculty of Applied Arts, Helwan University, Cairo, Egypt Abstract: Keywords: Fractals are a new branch of mathematics and art. But what are they really?, How Fractals can they affect on Furniture design?, How to benefit from the formation values and Mandelbrot Set properties of fractals in Furniture Design?, these were the research problem . Julia Sets This research consists of two axis .The first axe describes the most famous fractals IFS fractals were created, studies the Fractals structure, explains the most important fractal L-system fractals properties and their reflections on furniture design. The second axe applying Fractal flame functional and aesthetic values of deferent Fractals formations in furniture design Newton fractals inspired from them to achieve the research objectives. Furniture Design The research follows the descriptive methodology to describe the fractals kinds and properties, and applied methodology in furniture design inspired from fractals. Paper received 12th July 2016, Accepted 22th September 2016 , Published 15st of October 2016 nearly identical starting positions, and have real Introduction: world applications in nature and human creations. Nature is the artist's inspiring since the beginning Some architectures and interior designers turn to of creation. Despite the different artistic trends draw inspiration from the decorative formations, across different eras- ancient and modern- and the geometric and dynamic properties of fractals in artists perception of reality, but that all of these their designs which enriched the field of trends were united in the basic inspiration (the architecture and interior design, and benefited nature). from them by adding functional and aesthetic Mathematicians also had influenced by the values to design. nature's properties. They started from the past to So that the research studies the Fractals structure study the nature and conclusion the mathematics and their reflections to design furniture inspired relationships which explain its properties, and from them. analyses these relationships to get results that benefited the world generally and inspired the Problem: artists specially. 1. How can Fractals affect on Furniture The connection between mathematics and art goes design? back thousands of years. Mathematics has been 2. How to benefit from the formation values used in the design of Gothic cathedrals, Rose and properties of fractals in Furniture windows, oriental rugs, mosaics and tiling's. Design? Geometric forms were fundamental to the cubists Objectives: and many abstract expressionists, and award- 1. Inspiration from the geometric and winning sculptors have used topology as the basis dynamic properties of fractals in Furniture for their pieces. Dutch artist( M.C. Escher Design. )represented infinity, tessellations, deformations, 2. Appling functional and aesthetic values of reflections, Platonic solids, spirals, symmetry, and deferent Fractals formations in Furniture the hyperbolic plane in his works. http://www.ams.org/mathimagery/ Design. Only in the past century have mathematicians Importance: developed an understanding of such common 1. The research describes and analyzes the phenomena as snowflakes, clouds, coastlines, Fractals types and properties. lightning bolts, rivers, patterns in vegetation, and 2. Explanation the effect of Fractals on the trajectory of molecules in Brownian motion furniture design. (Dalton Allan- 2010). This branch of mathematics 3. Mentioning the applications of Fractals in is known as fractal. Fractals force us to alter our furniture and interior design. view of dimensionality, produce patterns from This work is licensed under a Creative Commons Attribution 4.0 International License Furniture design inspired from fractals 170 Hypotheses: The fractal is based upon an equation that Designing contemporary furniture inspired from undergoes an iteration or recursion – that is, a fractals adds functional and aesthetic values to repetition of itself. The object does not have to design. exhibit exactly the same structure on all scales, but the same type of structures must be apparent on all Methodology: scales for the structure to be considered a fractal The research follows the descriptive methodology (ERIN PEARSE, 2005). to describe the fractals kinds and properties and Benoit B. Mandelbrot (1924 –2010) was a Polish- applied methodology in furniture design inspired born, French and American mathematician with from fractals. broad interests in practical sciences, especially regarding what he labeled as "the art of roughness" Definition of Fractal: of physical phenomena. He referred to himself as "The term was coined by Benoît Mandelbrot* in a "fractalist"( Mandelbrot, Benoit (2012).He is 1975 and was derived from the Latin fractus recognized for his contribution to the field of meaning "broken" or "fractured. fractal geometry, which included coining the word The fractals are a never-ending pattern. They are "fractal'", as well as developing a theory of created by repeating a simple process over and "roughness and self-similarity" in nature. over in an ongoing feedback loop.( Martin Fractals kinds: (www.FractalFoundation.org- Churchill, 2004) 2009) The fractals are a geometrical shape that can be There are many different kinds of fractal images divided into parts, each of which is a smaller and can be subdivided into several groups. duplicate of the whole (Michael Frame - 2016). In Nature In Geometry In Algebra Fig.(1) Aloe Plant Fig.(2) Sierpinsky triangle Fig.(3) Mandelbrot set 1. Natural Fractals: (Michael Frame- 2016) International Design Journal, Volume 6, Issue 4 171 Rania Mosaad Saad 1. 1- Branching: lightning bolts, and river networks. Regardless of Fractals are found all over nature, spanning a huge scale, these patterns are all formed by repeating a range of scales. We find the same patterns again simple branching process. and again, from the tiny branching of our blood A fractal is a picture that tells the story of the vessels and neurons to the branching of trees, process that created it. Fig.(4) Neurons from the human Fig. (5) our lungs are branching Fig. (6) Lichtenberg " lightning" cortex. The branching of our brain fractals with a surface area~ 100m2 formed by rapidly discharging cells creates the incredibly The similarity to a tree is electrons in Lucite. complex network that is significant, as lungs and trees both responsible for all we perceive, use their large surface areas to imagine, remember. exchange oxygen and co2 . Fig.(7) river network in China, Fig.(8) Dragon tree, formed by a Fig.(9) fern leaves, formed by formed by erosion from repeated sprout branching, and then each of branching, and then each of the rainfall flowing dowenhill for the pranches branching again, etc. pranches branching again, etc. millions of years Fig.(4:9)Natural branching Fractals (www.FractalFoundation.org-2009) (Karl Richard- 2011) 1-2-Spirals: Fig.(10) A fossilized ammonite Fig.(11) A hurricane is a self- Fig.(12) A spiral galaxy is the from 300 million years ago. A organizing spiral in the atmosphere, largest natural spiral comprising simple, primitive organism, it built driven by the evaporation and hundreds of billions of stars its spiral shell by adding pieces condensation of sea water. that grow and twist at a constant rate. This work is licensed under a Creative Commons Attribution 4.0 International License Furniture design inspired from fractals 172 Fig.(13) The plant kingdom is full Fig.(14) The turbulent motion of Fig.(15) Snail shell is a self-similar of spirals. An agave cactus forms fluids creates spirals in systems that forms as a spiral of spirals of its spiral by growing new pieces ranging from a soap film to the spirals. rotated by a fixed angle. Many oceans, atmosphere and the surface other plants form spirals in this of jupiter way, including sunflowers, pinecones, etc. Fig.(10: 15)Natural spirals Fractals Richard- 2011) (www.FractalFoundation.org-2009) (Karl 2. Geometric Fractals: 2-1-IFS (iterated function systems): Fractals geometry, branch of mathematics concerned with irregular patterns made of parts that are in some way similar to the whole, a property called self-similarity or self-symmetry. Purely geometric fractals can be made by repeating a simple process. (www.FractalFoundation.org-2009) Fractals derived from standard geometry by using Fig. (17) Sierpinski triangle iterative transformations on an initial common figure like a straight line (the Cantor dust or the von Koch curve), a triangle (the Sierpinski triangle), or a cube (the Menger sponge).( Erin Pearse-2005) IFS fractals, as they are normally called, can be of any number of dimensions, but are commonly computed and drawn in 2D. The fractal is made up of the union of several copies of itself, each copy Fig. (18) Menger sponge being transformed by a function (hence "functions system"). (Draves, Scott- 2007). Fig. (16) von Koch curve Fig. (19) IFS being made with two functions. International Design Journal, Volume 6, Issue 4 173 Rania Mosaad Saad 2-2-L-system fractals: ( Stefan Kottwitz-2011) developed in 1968 by Aristid Lindenmayer, a An L-system or Lindenmayer system is consists of Hungarian theoretical biologist and botanist at an alphabet of symbols that can be used to the University of Utrecht. Lindenmayer used L- make strings, a collection of production rules that systems to describe the behavior of plant cells and expand each symbol into some larger string of to model the growth processes of plant symbols, an initial "axiom" string from which to development. L-systems have also been used to begin construction, and a mechanism for model the morphology of a variety of translating the generated strings into geometric organisms and can be used to generate self- structures. L-systems were introduced and similar fractals such as iterated function Fig. (20) The dragon curve drawn using an L-system. Fig. (21) Pythagoras tree by L-system. 3. Algebraic Fractals: "We can also create fractals by repeatedly plane. The equation gives an answer, ‘Znew’ . We calculating a simple equation over and over.